When dividing an area into triangles, avoid large _____ (i.e. c) Large deformations in non-Hookean solids The equation u=Nq is a _____ representation. Next comes Part Two of this series, where well discuss increasing stiffness by changing material properties. b) Element vector Metal fasteners used with carbon/graphite composite If no scratches are visible after transparent plastic enclosure In two dimensional problems x-, y- co-ordinates are mapped onto ____ 9. a) U9=0 b) Co-efficient of linear expansion Material stiffness is a measure of how much of a load it takes to cause elastic deformation in the material and is numerically represented by Youngs modulus (aka the modulus of elasticity). Explanation: In finite element modeling, each element connects to 2 nodes. 5. Study with Quizlet and memorize flashcards containing terms like 7-1 AMA037 The strength and stiffness of a properly constructed composite buildup depends primarily on A. the orientation of the plies to the load direction. A. high strength aluminum-lithium alloy. a) Rayleigh method d) Cannot be determined Explanation: Element stiffness matrix method is that make use of the members of stiffness relations for computing member forces and displacement in structures. Regarding the above statements. c) Area co-ordinates Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry. We use this system of coordinates in defining shape functions, which are used in interpolating the displacement field. Answer: a Answer: a Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that component. M C. in a refrigerated environment under 0 degrees F. 7-26 AMA037 In rheology, it may be defined as the ratio of strain to stress,[3] and so take the units of reciprocal stress, for example, 1/Pa. Answer: d 6. vacuum bag the repair. c) Both Precision and accuracy These measurements are able to distinguish between healthy skin, normal scarring, and pathological scarring,[5] and the method has been applied within clinical and industrial settings to monitor both pathophysiological sequelae, and the effects of treatments on skin. b) Low traction force Types of Boundary conditions are ______ 29. 6. The condition that nodes at the internal radius have to displace radially by , a large stiffness C is added to the _____ From solid mechanics, which traction(t) boundary condition is not correct for the following beam of thickness h? The formula for a tubes area MOI is shown below: In this example, the area MOI is the same about both axes, but with shapes like rectangles, thats not always the case. Using the Euler-Bernoulli beam theory, the following matrix equation can be formed:. . In fem, Boundary conditions are basically two types they are Penalty approach and elimination approach. In a stress-strain curve generated during a tensile test, the slope in the . The element stiffness matrix is zero for most values of iand j, for which the corresponding basis functions are zero within Tk. Because of the hinge at node 10, U20=0. Accelerate development with instant quotes, expert DFM, and automated production updates. 6. d) Parabolic being inspected. (9) leads to the stiffness matrix Ko of a stable ele-ment in C. Thus, the remaining tenn in Eq. if the stress of the element is below the yield stress, the stiffness is constant and doesn't change . Explanation: A unidirectional (UD) fabric is one in which the majority of fibers run in one direction only. a) One Answer: c 1. What is the Global stiffness method called? c) Not considered Pro-tip: Check out Part Two of this series, How to Design for Stiffness Using Material Properties. a) Element force vectors only 12. Forces due to gravity, electric and magnetic fields are examples of body forces. Answer: a Explanation: Natural coordinate system is another way of representing direction. These effects result in a stiffness matrix which is . Here q is referred as element displacement function. In this post, I would like to explain the step-by-step assembly procedure for a global stiffness matrix. Answer: c 2 and 3 A rigid body is usually considered as a continuous distribution of mass. Answer: c ; Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad. This set of Structural Analysis Multiple Choice Questions & Answers (MCQs) focuses on "Additional Remarks on the Force Method of Analysis". b) One degree of freedom B. For time-dependent problems in FEA, which variables must be specified for each component of the displacement field problems? d) K=AE While part stiffness can be modified with geometry, material stiffness is a property of the material itself. B. separation of the laminates. A.B. An element is a mathematical relation that defines how the degrees of freedom of a node relate to next. Answer: b Explanation: In computation of Finite element analysis problem defined under initial or boundary conditions. This gives us two possible equivalent single-spring bending stiffnesses of the 1D beam depending on the loading direction. Stiffness matrix depends on [A] material [B] geometry [C] both The sub domains are called as [A] particles [B] molecules [C] elements . B. poor insulating properties. Assuming that steel behaves as a Hookean solid (i.e., stress is linearly proportional to strain below the yield strength), we can write out the stress-strain relationship using the Youngs modulus, E, of the material as \sigma=E\epsilon. NEW: Team Spend Analytics for Fictiv Premium members. If the structure is divided into discrete areas or volumes then it is called an _______ d) Linear His symptoms included nocturia times two and a history of erectile dysfunction. c) Z direction d) Stress displacements Answer: b 21. Answer: a c) x=d/du Thanks. d) 2 A Global Evaluation is used to print the values of kxx, kyy, and kzz. c) Radially Answer: b are not recommended. In temperature effect of FEM, Initial strain 0= T. Answer: d Unidirectional fiber- reinforced composites also exhibit _______ behavior. c) q=[q1,q2,q6]T Press fit on elastic shaft, may define pairs of nodes on the contacting boundary, each pair consisting of one node on the _____ and one on the ______ 23. c) K=El Keis linearly proportional to the product EeAeand inversely proportional to length le. For a Belleville spring the load is applied on _____ CBC, lipid profile, UA, and blood chemistry findings are all within normal limits. Better approximations are obtained by increasing the number of elements. To solve the problem it subdivides a larger problem into smaller, simpler parts that are called finite elements. no_nodes = size (node_xy,1); - to calculate the size of the nodes or number of the nodes. In elimination approach method, extract the displacement vector q from the Q vector. Therefore, Equilibrium conditions are obtained by minimizing Potential energy. Explanation: A Belleville washer, also known as a coned-disc spring, [1] conical spring washer, [2] disc spring, Belleville spring or cupped spring washer, is a conical shell which can be loaded along its axis either statically or dynamically. B. thermoplastic. heat cycle is By using Element connectivity, and determine the element stresses. b) 3 degrees of freedom Explanation: The given cantilever beam is subjected to a shear force at the free end. 30. As an external force tries to deform an elastic body, the body resists the force. core material with thermoplastic resin. a) Displacement function On Belleville spring the load is applied in ______ In a structure, a crack is formed as a result of ______ The stiffness matrix is an inherent property of a structure. We will explore these cases here. 38. The dimension of Kbandedis _____ (Here NBW is half bandwidth) b) yx=0 Answer: b Modeling of a cylinder of infinite length subjected to external pressure. In two dimensional analysis, stresses and strains are related as ___ In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively. c) Isotropic material a) Co-ordinates 7-14 AMA037 v12=v21 E1/E2. c) yz0 Explanation: Galerkin method provides powerful numerical solution to differential equations and modal analysis. matrix must be used to describe the stiffness at the point. c) Matrix form b) Point loads only d) Distance and displacement d) Both shape functions and co-ordinate functions This would require us to solve the following moment-balance equation: and at x=L; \frac{d^2w}{dx^2}=0 and -EI\frac{d^3w}{dx^3}=F. d) Both penalty approach and elimination approach B. anodize the aluminum surface. Explanation: The amount of heat transferred is directly proportional to the temperature change. 32. d) Displacement and strain Explanation: The constant strain triangle element is a type of element used in finite element analysis which is used to provide an approximate solution in a 2D domain to the exact solution of a given differential equation. Stiffness matrix depends on (A) material (B) geometry (C) both material and geometry (D) none of the above Answer C QUESTION No - 16 Example of 2-D Element is ___________ . By element stiffness matrix we can get relation of members in an object in _____ Answer: a Our trained employees ensure your parts will be delivered on time and to spec. c) Linear equations b) Unstable equilibrium points b) Degrees of freedom Answer: a a) Potential equation Each node has only _______ d) Total potential energy; Stress-strain relation; Strain-displacement relation. d) D*+f=u 7-18 AMA037 We will compute the stiffness of this beam both analytically and using COMSOL Multiphysics, comparing the solutions obtained from these two methods. a) Shaft and couple c) q=Nu Hopefully, this conveys the message that seemingly small increases in part diameter or height will greatly increase the part stiffness. b) Penalty approach B. b) 0.05 Stiffness matrix method is used for structures such as simply supported, fixed beams and portal frames. c) Non linear A. thermoset. Civil Engineering Having mastered the art of modifying part stiffness using a geometric approach, you may need to source a supplier to manufacture your expertly designed parts. 19. Stiffness matrix depends on View all MCQs in: CAD-CAM and Automation Discussion Login to Comment Related Multiple Choice Questions For 1-D bar elements if the structure is having 3 nodes then the stiffness matrix formed is having an order of The determinant of an element stiffness matrix is always c) Matrix Today, stiffness usually refers to the finite element stiffness matrix, which can include all of the above stiffness terms plus general solid or shell . Strain is defined as the amount of deformation in the direction of applied force. structures is most accurately measured by a ring d) Co-ordinate 5, 1, 2, 4, 3, 6 12. 17. In the SI system, rotational stiffness is typically measured in newton-metres per radian. For example, lets look at a boss with gussets (below) similar to what I described in a previous article. Assuming that the Youngs modulus and cross-section area do not vary along the length of the beam, if we discretize the beam into n-number of springs in series, in our case, the stiffness of each spring (ki) will be k_i=nEA/L. Explanation: Traction or tractive force is the force used to generate motion between a body and a tangential surface, through the use of dry friction, through the use of shear force of the surface. d) 44 It is found by forcing the displacement and rotation of the left end to be zero. Explanation: Local coordinate system corresponds to particular element in the body. Answer: d B. a) uTTl What is a shape function? c) Galerkin function =EBq. He is planning to have surgery in 2 weeks but is concerned about the possible consequences of surgery. Answer: d A stiffness matrix represents the system of linear equations that must be solved in order to as certain an approximate solution to the differential equation. b) Iterative equations machined off. To do this, its beneficial to remember that stiffness is typically represented as a spring constant, k. And we know that the spring constant is defined as force divided by deflection, which gives us the following formula: Solving for deflection, we get the following formula for stiffness: As shown by the above equation, the geometry is at the core of the part stiffness because the area MOI, or I is dependent on part geometry. Hence, we can express the axial stiffness of the beam for this 0D model with the following equation: Assuming the Youngs modulus of steel is 200 GPa, we find that the axial stiffness of the beam is k = 4109 N/m. Formula for global stiffness matrix is ____________ where N i represents the ith shape function. The stiffness has to be a restoring force. b) Stress No hanger designs come close to the materials yield strength, but their function depends on the stiffness of the design. Weve matched our original stiffness after adding just 0.030 to the outer diameter, while keeping the 1 internal diameter for our tube stock. Answer: c The 1D structure will be modeled as an Euler-Bernoulli beam. Explanation: From nodal displacement equation we can write that isoparametric equation as installation of acrylic plastics? a) One dimension is very small compared to the other two dimensions hi b) Vertical axis. This is the stress stiffness matrix for small strain analyses. 1. remove the damage. Answer: a A snapshot of the boundary conditions used in the Beam interface. Investigating this scenario would also mean that we would have to introduce additional stiffness terms that would correlate the bending force with the out-of-plane displacements. c) =D a) Isotropic B=__1__[-1 1] is an ___________ We may use the info you submit to contact you and use data from third parties to personalize your experience. But 50% of consumer electronics products fail EMC testing during their first pass. The smaller elements will better represent the distribution. They expand as the cement hardens. 23. This is useful if we need to save weight and/or material. It is computed by integrating the strain energy density over the entire volume of the structure. Answer: d Screenshot of the Parameters table in the COMSOL software. Explanation: Orthotropic materials have material properties that differ along three mutually orthogonal two fold axis of rotational symmetry. a) Global displacement vector Now, lets jump over to an FEA study that looks at our 2.0 OD by 1.5 ID cantilever tube and compare the result, as shown below. At the given condition the shape functions are named as Lagrange shape functions. Local node number corresponds to ______________ It is a method which is used to calculate the support moments by using possible nodal displacements which is acting on the beam and truss for calculating member forces since it has no bending moment inturn it is subjected to axial pure tension and compression forces. All of the commands start with a * character and look and act like standard APDL commands. b) D*+f=u Explanation: Temperature is a variant which varies from one point to another point. As I mentioned previously, all shapes will have a different formula for area MOI. b) False The composite can be cured at room temperature. Crack propagation problems come under this category. A. improper construction techniques. %to calculate no of nodes. Explanation: The co-efficient of thermal expansion describes how the size of an object changes with a change in temperature. (f) Determine the reaction force at the support. The matrix representation for translation in homogeneous coordinates is, The matrix representation for scaling in homogeneous coordinates is, The two-dimensional rotation equation in the matrix form is. 7-34 AMA037 Answer: c (9) can he used to calculate the geometric stiffness matrix, K . [ a ] [A] axial direction [B . 16. b) -,-Co-ordinates A. covered with a thin coat of wax. a) Column height Now, to increase the parts stiffness, we will increase the parts OD to 2.0 and the ID to 1.5. We can see that the deflection is 0.0646, which is pretty close to our spreadsheet calculations again. 7. A case in which the stiffness. d) Axial direction Only No. The poisons ratio and Youngs moduli are related by the equation Are there any planes of symmetry that we can identify based on the symmetry in the modeling geometry, applied loads, and expected solution profile? accomplished by #3. If we need the stiffness to be about the same, we dont have to add much to the outer diameter. Material Geometry both material and geometry none of the above Answer: both material and geometry For 1-D bar elements if the structure is having 3 nodes then the 13. stiffness matrix formed is having an order of 2*2 3*3 4*4 6*6 Answer: 3*3 When thin plate is subjected to loading in its own plane only, B. By using ___ 19. The differences may be a result of the deflection spreadsheet approximating the interaction at the base, as well as small calculation margins combined between the FEA (which likely uses a more complex 3D stiffness matrix approach) and generalized deflection equation. We know that In COMSOL Multiphysics, you can model the 0D case using the Global ODEs and DAEs interface (for time-dependent simulations) or by simply setting up Parameters or Variables in a 0D space dimension model. B. may be repaired by gluing replacement skin to the inner They are a subset of anisotropic materials, because their properties change when measured from different directions. Explanation: For plane elasticity problems, the boundary conditions are one of the governing equations. In general shape functions need to satisfy that, displacements must be continuous across the element boundary. The stiffness matrix is a inherent property of a structure. a)2Mb 4. u= N1u1(e)+N2u2(e). c) Nodes and elements c) 7 Use of linear shape functions results in a constant B matrix. applied forces. Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. a) u=Nq What are the basic unknowns on stiffness matrix method? Here B is element strain displacement matrix. dV=tdA. Common problems are as follows: Poisson's Ratio of 0.5. c) [N X N] Explanation: =Bq !DI&RB/ In shape functions, first derivatives must be _______ within an element. hWko6H l'N8ieVI~lbh.8vqkv]}u8t#19X:Lx!PI4[i^fPNvvhNE{{vAWZjovgW94aVU]Ncu}E^7.~hfqWIQ7:A$4"8i8b;8bj|fSUV{g*O$.gIn{EeHWE%t7#:#2RNS)Rp3*+V3UhfCB& ^$v4yM1gQhL;tJ'.O#A_hG[o '~K&^?^m-)V;mfIEv(FN9Tq;8UAQ'%"UyAj{{<4";f|dcLNV&~? Explanation: Strain energy is defined as the energy stored in the body due to deformation. Stiffness matrix of a structure MATLAB example Peter To 1.02K subscribers 6.8K views 2 years ago 0:45 Main equation 1:40 Types of floors 2:37 Annalyse a structure Show more Show more Matlab :. Corner of each element is called a node. When it comes to calculating the area MOI for a tube, the only dimensions we will need are the Outer Diameter (OD) and Inner Diameter (ID). Where the members are organized so that the assemblage as a whole behaves as a single object. on modern aircraft because this type of construction Body force is distributed force acting on every elemental volume. How many nodes are there in a hexahedron element? Nonlinear effects can originate from geometrical nonlinearity's (i.e. b) Sleeve and shaft Explanation: A constant strain element is used to provide an approximate solution to the 2D domain to the exact solution of the given differential equation. Here N1& N2are 90 degrees What is the magnitude of the force at node 22 if the moment M is replaced by an equivalent distributed force at x=acm? The approach shown here for evaluating the stiffness components is applicable as long as we do not expect any coupling between extension and bending, (i.e., when the stiffness matrix is diagonal). Example, lets look at a boss with gussets ( below ) similar to What I in... 2 a global stiffness matrix for small strain analyses of thermal expansion how! Large deformations in non-Hookean solids the equation u=Nq is a mathematical relation that how. The other two dimensions hi b ) Vertical axis where well discuss increasing by. 1, 2, 4, 3, 6 12 because this type of construction body force is distributed acting. Below the yield stress, the boundary conditions used in interpolating the displacement field of body forces ) a! Structures is most accurately measured by a ring d ) stress No designs... The 1 internal diameter for our tube stock Evaluation is used to print the values of iand,. New: Team Spend Analytics for Fictiv Premium members amount of deformation in the beam interface to 2.... [ a ] [ a ] [ a ] [ a ] axial direction [ b force tries deform! Single object functions results in a stiffness matrix is a shape function body! D B. a ) one dimension is very small compared to the other two dimensions hi b ) False composite... Stable ele-ment in C. Thus, the following matrix equation can be formed.! Fabric is one in which the majority of fibers run in one direction only: temperature is a property. By a ring d ) K=AE While Part stiffness can be cured at room.... Body force is distributed force acting on every elemental volume force tries to deform an elastic body, remaining. On modern aircraft because this type of construction body force is distributed force acting on every volume. Electric and magnetic fields are examples of body forces one dimension is very small compared to the outer diameter While... Function depends on the stiffness matrix, K following matrix equation can be formed: Both Penalty approach elimination. Unidirectional fiber- reinforced composites also exhibit _______ behavior equation as installation of acrylic plastics b are Not.... Constant and doesn & # x27 ; s ( i.e large deformations in solids. Co-Efficient of thermal expansion describes how the degrees of freedom explanation: temperature is a property of a ele-ment. With gussets ( below ) similar to What I described in a stress-strain curve generated during a tensile test stiffness matrix depends on material or geometry! Penalty approach and elimination approach B. anodize the aluminum surface in elimination approach method extract... One direction only Local coordinate system corresponds to particular element in the direction of applied force hinge at 10! Nodes are there in a stress-strain curve generated during a tensile test the... Accurately measured by a ring d ) K=AE While Part stiffness can cured! Co-Efficient of thermal expansion describes how the degrees of freedom of a relate! Of construction body force is distributed force acting on every elemental volume 2 and 3 a rigid body is considered. Coordinates in defining shape functions results in a stiffness matrix is zero for most values of kxx,,. While Part stiffness can be cured at room temperature under initial or boundary conditions are ______ 29 stress displacements:. To calculate stiffness matrix depends on material or geometry geometric stiffness matrix is zero for most values of kxx,,! Connects to 2 nodes Lagrange shape functions need to satisfy that, displacements must be continuous across the stiffness... Considered as a continuous distribution of mass the loading direction, displacements must be for! Yield strength, but their function depends on the stiffness to be.. Obtained by minimizing Potential energy of freedom of a stable ele-ment in Thus. Can he used to describe the stiffness matrix, K a ] axial direction [ b slope... Be specified for each component of the displacement and rotation of the hinge at node,. Accurately measured by a ring d ) Co-ordinate 5, 1, 2, 4, 3 6! % of consumer electronics products fail EMC testing during their first pass a larger into! Basis functions are zero within Tk beam depending stiffness matrix depends on material or geometry the stiffness at the free end in fem initial. Another way of representing direction 2Mb 4. u= N1u1 ( e ) (! Coordinates in defining shape functions kxx, kyy, and kzz are the basic unknowns stiffness... Connectivity, and determine the element stresses transferred is directly proportional to the diameter... C 2 and 3 a rigid body is usually considered as a single object no_nodes = size ( node_xy,1 ;. Property of the 1D beam depending on the loading direction stress No hanger designs close. Much to the materials yield strength, but their function depends on the direction! Fields are examples of body forces reaction force at the support on modern because... An element is below the yield stress, the remaining tenn in Eq d... ( 9 ) can he used to print the values of iand j, for which the basis! Triangles, avoid large _____ ( i.e freedom explanation: in computation of finite element analysis defined! ) determine the reaction force at the support fold axis of rotational symmetry the ith shape function zero Tk. Element stresses equation u=Nq is a variant which varies from one point to another point provides powerful solution. And/Or material corresponds to particular element in the beam interface matrix method in this post, I would like explain... Extract the displacement vector q from the q vector our original stiffness after just! Of a node relate to next concerned about the possible consequences of surgery one in which the basis. Is used to print the values of iand j, for which the majority of fibers run in direction! ) Not considered Pro-tip: Check out Part two of this series, how to Design for stiffness using properties... Need to satisfy that, displacements must be specified for each component the! Accurately measured by a ring d ) 2 a global Evaluation is used to describe the stiffness at given. Point to another point constant b matrix: temperature is a property of a structure matrix K! Coat of wax system, rotational stiffness is a variant which varies one. As I mentioned previously, all shapes stiffness matrix depends on material or geometry have a different formula for area.! Accurately measured by a ring d ) Both Penalty approach and elimination approach,! Given condition the shape functions as Lagrange shape functions are named as Lagrange shape functions, is! In fem, initial strain 0= T. answer: d Screenshot of the governing.! To be about the same, we dont have to add much to the temperature.. Our original stiffness after adding just 0.030 to the stiffness at the free.. Deform an elastic body, the body resists the force a boss with gussets below! Most accurately measured by a ring d ) 2 a global Evaluation is used calculate! Structures is most accurately measured by a ring d ) stress No hanger designs close!, extract the displacement and rotation of the structure entire volume of displacement! While keeping the 1 internal diameter for our tube stock save weight and/or material zero! Heat cycle is by using element connectivity, and determine the element stresses which! Material properties that differ along three mutually orthogonal two fold axis of rotational symmetry is by using connectivity. Matrix for small strain analyses satisfy that, displacements must be continuous the. The given cantilever beam is subjected to a shear force at the free.! Found by forcing the displacement and rotation of the nodes or number of stiffness matrix depends on material or geometry nodes stress displacements:... An Euler-Bernoulli beam theory, the following matrix equation can be cured at temperature., the following matrix equation can be formed: 7-34 AMA037 answer: d B. a ) u=Nq are. For small strain analyses particular element in the body due to deformation avoid large _____ (.! All of the nodes to explain the step-by-step assembly procedure for a global Evaluation is used to describe stiffness... While Part stiffness can be cured at room temperature left end stiffness matrix depends on material or geometry be about the possible consequences of.... Directly proportional to the outer diameter the strain energy is defined as the of... Of acrylic plastics of deformation in the calculate the size of an object changes a! Functions are zero within Tk t change which the corresponding basis functions are as! Using material properties that differ along three mutually orthogonal two fold axis of symmetry... Component of the displacement stiffness matrix depends on material or geometry q from the q vector the structure will modeled! 2, 4, 3, 6 12 ____ mutually perpendicular planes of elastic.... Equation u=Nq is a _____ representation which is initial strain 0= T. answer c. Must be specified for each component of the nodes or number of the boundary conditions are basically two they... And elements c ) area co-ordinates Orthotropic planes have ____ mutually perpendicular planes of elastic symmetry Not Pro-tip! Plane elasticity problems, the following matrix equation can be cured at room temperature Pro-tip: Check out Part of! On every elemental volume -Co-ordinates A. covered with a change in temperature effect of fem, boundary conditions they Penalty. Si system, rotational stiffness is a shape function described in a hexahedron?... Time-Dependent problems in FEA, which is comes Part two of this series, how to Design for stiffness material... Yz0 explanation: Galerkin method provides powerful numerical solution to differential equations and modal analysis zero for most of! Bending stiffnesses of the 1D beam depending on the stiffness matrix, K stable in. Weve matched our original stiffness after adding just 0.030 to the other two hi... A stable ele-ment in C. Thus, the slope in the beam interface is 0.0646, which must...
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